### Information fusion with belief functions: A DSmT perspective International Workshop on Information Fusion

Jean Dezert
unpublished
m = 1, . . . , p are disjunctions of elements θ i , (i ∈ {1, . . . , n} of the fram , the s sources are in total conflict and their combination ca mathematically not defined due to 0/0 indeterminacy . DS rule is commu Dempster's rule of combination r's rule of combination r's rule of combination, denoted DS rule 5 is a mathematical operation, represented to the normalized conjunctive fusion rule. Based on Shafer's model of Θ, the combin sources of evidences characterized by their bba m 1
more » ... y their bba m 1 (.), . . . , m s (.) related to the same S (.) = [m 1 ⊕ . . . ⊕ m s ](.). The quantity m DS (.) is defined mathematically as follows: it DS rule because it has been proposed historically by Dempster , , and widely promoted by Shafer in Belief functions and DST Combination of two distinct sources of evidence DS rule = Normalized conjunctive rule 12 X 1 ,X 2 ∈2 X 1 ∩X 2 =X Conjunctive fusion X 1 ,X 2 ∈2 X 1 ∩X 2 =∅ Conflict level DS rule = normalized conjunctive fusion rule Properties: extension to n > 2 sources; associativity; commutativity; neutrality of vacuous bba [m ⊕ m v ](.) = m(.) Conditioning: m(.) combined with m Z (.) focused on Z (i.e. m Z (Z ) = 1) DS rule yields m(X |Z ) = [m ⊕ m Z ](X ) = [m Z ⊕ m](X ) and Pl(X |Z ) = Pl(X ∩ Z )/Pl(Z ) (similar to Conditioning rule for probas). Drawbacks: Counter-intutitive and unexpected behaviors in some cases validity of DS rule has become very questionable over the years ... at le for highly conflicting cases. Conflict level DS rule = normalized conjunctive fusion rule Properties: extension to n > 2 sources; associativity; commutativity; neutrality of vacuous bba [m ⊕ m v ](.) = m(.) Conditioning: m(.) combined with m Z (.) focused on Z (i.e. m Z (Z ) = 1) with DS rule yields m(X |Z ) = [m ⊕ m Z ](X ) = [m Z ⊕ m](X ) and Pl(X |Z ) = Pl(X ∩ Z )/Pl(Z ) (similar to Conditioning rule for probas). Drawbacks: Counter-intutitive and unexpected behaviors in some cases ⇒ validity of DS rule has become very questionable over the years ... at least for highly conflicting cases.